ដោះស្រាយ 945=1000*xdiv2*(1-1.042^-21)div0.042+1000div1.042^21

$$945=1000 \times x \div 2 \times (1- { 1.042 }^{ -21 } ) \div 0.042+1000 \div { 1.042 }^{ 21 }$$

ដោះស្រាយសម្រាប់ x

$$x=\frac{118455359078051916563803951486093011267876770521240512800069}{1558334187683122846608767340464764566236794791146894845050000}\approx 0.076014092$$

ជំហានសម្រាប់ការដោះស្រាយសមីការលីនេអ៊ែរ

ចែក 1000x នឹង 2 ដើម្បីបាន500x។

$$945=\frac{500x\left(1-1.042^{-21}\right)}{0.042}+\frac{1000}{1.042^{21}}$$

គណនាស្វ័យគុណ 1.042 នៃ -21 ហើយបាន \frac{476837158203125000000000000000000000000000000000000000000}{1131337517030036595575682282995201117819453812281695834921}។

$$945=\frac{500x\left(1-\frac{476837158203125000000000000000000000000000000000000000000}{1131337517030036595575682282995201117819453812281695834921}\right)}{0.042}+\frac{1000}{1.042^{21}}$$

ដក​ \frac{476837158203125000000000000000000000000000000000000000000}{1131337517030036595575682282995201117819453812281695834921} ពី 1 ដើម្បីបាន \frac{654500358826911595575682282995201117819453812281695834921}{1131337517030036595575682282995201117819453812281695834921}។

$$945=\frac{500x\times \frac{654500358826911595575682282995201117819453812281695834921}{1131337517030036595575682282995201117819453812281695834921}}{0.042}+\frac{1000}{1.042^{21}}$$

គុណ 500 និង \frac{654500358826911595575682282995201117819453812281695834921}{1131337517030036595575682282995201117819453812281695834921} ដើម្បីបាន \frac{327250179413455797787841141497600558909726906140847917460500}{1131337517030036595575682282995201117819453812281695834921}។

$$945=\frac{\frac{327250179413455797787841141497600558909726906140847917460500}{1131337517030036595575682282995201117819453812281695834921}x}{0.042}+\frac{1000}{1.042^{21}}$$

ចែក \frac{327250179413455797787841141497600558909726906140847917460500}{1131337517030036595575682282995201117819453812281695834921}x នឹង 0.042 ដើម្បីបាន\frac{7791670938415614233043836702323822831183973955734474225250000}{1131337517030036595575682282995201117819453812281695834921}x។

$$945=\frac{7791670938415614233043836702323822831183973955734474225250000}{1131337517030036595575682282995201117819453812281695834921}x+\frac{1000}{1.042^{21}}$$

គណនាស្វ័យគុណ 1.042 នៃ 21 ហើយបាន 2.372586736514575306484733251147952014637303201334182983596244992។

$$945=\frac{7791670938415614233043836702323822831183973955734474225250000}{1131337517030036595575682282995201117819453812281695834921}x+\frac{1000}{2.372586736514575306484733251147952014637303201334182983596244992}$$

ពង្រីក \frac{1000}{2.372586736514575306484733251147952014637303201334182983596244992} ដោយគុណទាំងភាគបែង និងភាគយកជាមួយនឹង 1000000000000000000000000000000000000000000000000000000000000000។

$$945=\frac{7791670938415614233043836702323822831183973955734474225250000}{1131337517030036595575682282995201117819453812281695834921}x+\frac{1000000000000000000000000000000000000000000000000000000000000000000}{2372586736514575306484733251147952014637303201334182983596244992}$$

កាត់បន្ថយប្រភាគ \frac{1000000000000000000000000000000000000000000000000000000000000000000}{2372586736514575306484733251147952014637303201334182983596244992} ទៅតួដែលតូចបំផុតដោយ​ដក និងលុបចេញ 2097152។

$$945=\frac{7791670938415614233043836702323822831183973955734474225250000}{1131337517030036595575682282995201117819453812281695834921}x+\frac{476837158203125000000000000000000000000000000000000000000000}{1131337517030036595575682282995201117819453812281695834921}$$

ប្ដូរផ្នែកទាំងពីរ ដើម្បីឲ្យតួអថេរទាំងអស់ស្ថិតនៅផ្នែកខាងឆ្វេង។

$$\frac{7791670938415614233043836702323822831183973955734474225250000}{1131337517030036595575682282995201117819453812281695834921}x+\frac{476837158203125000000000000000000000000000000000000000000000}{1131337517030036595575682282995201117819453812281695834921}=945$$

ដក \frac{476837158203125000000000000000000000000000000000000000000000}{1131337517030036595575682282995201117819453812281695834921} ពីជ្រុងទាំងពីរ។

$$\frac{7791670938415614233043836702323822831183973955734474225250000}{1131337517030036595575682282995201117819453812281695834921}x=945-\frac{476837158203125000000000000000000000000000000000000000000000}{1131337517030036595575682282995201117819453812281695834921}$$

ដក​ \frac{476837158203125000000000000000000000000000000000000000000000}{1131337517030036595575682282995201117819453812281695834921} ពី 945 ដើម្បីបាន \frac{592276795390259582819019757430465056339383852606202564000345}{1131337517030036595575682282995201117819453812281695834921}។

$$\frac{7791670938415614233043836702323822831183973955734474225250000}{1131337517030036595575682282995201117819453812281695834921}x=\frac{592276795390259582819019757430465056339383852606202564000345}{1131337517030036595575682282995201117819453812281695834921}$$

ចែកជ្រុងទាំងពីនឹង \frac{7791670938415614233043836702323822831183973955734474225250000}{1131337517030036595575682282995201117819453812281695834921}។

$$x=\frac{\frac{592276795390259582819019757430465056339383852606202564000345}{1131337517030036595575682282995201117819453812281695834921}}{\frac{7791670938415614233043836702323822831183973955734474225250000}{1131337517030036595575682282995201117819453812281695834921}}$$

បង្ហាញ \frac{\frac{592276795390259582819019757430465056339383852606202564000345}{1131337517030036595575682282995201117819453812281695834921}}{\frac{7791670938415614233043836702323822831183973955734474225250000}{1131337517030036595575682282995201117819453812281695834921}} ជាប្រភាគទោល។

$$x=\frac{592276795390259582819019757430465056339383852606202564000345}{1131337517030036595575682282995201117819453812281695834921\times \frac{7791670938415614233043836702323822831183973955734474225250000}{1131337517030036595575682282995201117819453812281695834921}}$$

គុណ 1131337517030036595575682282995201117819453812281695834921 និង \frac{7791670938415614233043836702323822831183973955734474225250000}{1131337517030036595575682282995201117819453812281695834921} ដើម្បីបាន 7791670938415614233043836702323822831183973955734474225250000។

$$x=\frac{592276795390259582819019757430465056339383852606202564000345}{7791670938415614233043836702323822831183973955734474225250000}$$

កាត់បន្ថយប្រភាគ \frac{592276795390259582819019757430465056339383852606202564000345}{7791670938415614233043836702323822831183973955734474225250000} ទៅតួដែលតូចបំផុតដោយ​ដក និងលុបចេញ 5។

$$x=\frac{118455359078051916563803951486093011267876770521240512800069}{1558334187683122846608767340464764566236794791146894845050000}$$